Here where I live a similar thing exists for like 10 years already, and if the recepient has 2 bank accounts from different banks, then the banking app lets you choose which bank you want to send the money to. They also show the recipient's first and middle names (only the first letter of the last name is shown) to make sure you're sending money to the right person.

And I've always wondered, isn't it kind of unsafe, if someone gets my number, they can learn where I store my money and what my name is.

Dunno about the desktop, but if you're on a phone, there's often a button "open in the bank app". I actually like that you need to approve it in the banking app, it's like a single source of truth no one else but me has access to. Dunno why it would be "way slower", it's just an additional click?